Disk drives include both separate servo tracks and "embedded" servo tracks to enable position error signals to be derived which are then used to control the position of a head/arm actuator to achieve improved head/track alignment. Servo data generally contains two bursts of data that are offset on either side of a track's center line. If a transducer head is properly positioned with respect to a track's center line, signals derived from offset bursts in the servo track are equal and no corrective operation is required. If there is an inequality in the sensed signals, the inequality is converted to a digital value and is fed to a correction or compensating circuit which generates a correction voltage that is fed to the head/arm actuator. The correction voltage preferably enables the head to be properly re-positioned with as little undershoot or overshoot as possible.
The correction circuit, if properly designed, enables positioning of a transducer head over a track's center line (i) if the track is nonconcentric, (ii) if the head/arm structure is subject to vibration or shock or (iii) if other noise is present in the servo signal which gives rise to a manifestation of a mispositioning of the head.
Referring to FIG. 1, a prior art control system is illustrated and includes a head/arm actuator 10 and a transducer head 12 that is positioned over a disk 14. When transducer head 12 is positioned over servo information, a signal is fed, via a demodulator 15, to a sense amplifier 16 and thence, via an analog to digital (A/D) converter 18, to a compensator 20. In addition, the output from A/D converter 18 is fed to a processor 22 where the digitized data values are stored in a memory 24. In order to cause actuator 10 to move transducer head 12 to a specified track, an address is fed from processor 22 to an actuator control circuit 26 which, in turn, operates actuator 10 to position transducer head 12 over the track indicated by the address. Included, but not shown, in actuator 10 is a digital to analog converter.
In FIG. 2, a prior art control schematic illustrates a compensator 20 and plant 30. Plant 30 includes actuator control 26, actuator 10 and transducer head 12 as shown in FIG. 1. Compensator 20 is represented in the control schematic by an infinite impulse response (IIR) filter 32 and a finite impulse response (FIR) filter 34. Filters 32 and 34 are represented as second order filters in that each is provided with a pair of unit time segment delay elements z.sup.-1. FIR filter 34 includes three adjustable gain stages Cf0, Cf1, Cf2. IIR filter 32 includes a pair of adjustable gain stages Cb1 and Cb2. A summer 36 serves as an input node for compensator 20 and a summer 38 provides an output node therefor. The output from summer node 38 is fed back to the unit time delay elements in IIR filter 32 to enable a continued filtering action to be accomplished.
Those skilled in the art will realize that the control schematic illustration of compensator 20 is merely representative of the functions that are performed therein. In general, those functions will be performed by an appropriately programmed digital signal processor which will insert the proper time delays and gain values for the various gain stages to enable the filtering actions to be accomplished.
The output from compensator 20 is fed through a summing node 40 which serves also as an input point for an externally applied acceleration disturbance signal A(k). Plant 30 receives the input from summer 40, reacts to that input (and any disturbance contained therein) and provides an output response signal to summer node 42. A further input to summer node 42 is a desired position value (generally equal to 0) which enables the output of summer 42 to manifest a position error signal (PES) over each of a plurality of time intervals O-k. Each PES(k) value (for each k time) is fed back to summer 36. There the fed back value is subjected to a filtering action within compensator 20 in accordance with the gain values present in each of the component gain stages.
In order to enable adjustment of each of the gain stages in compensator 20, the prior art teaches that a "least mean squares" (LMS) algorithm provides a means for calculating appropriate adjustments. The LMS algorithm adjusts coefficients of an FIR/IIR filter by adjusting them in proportion to the inputs, scaled by an error value and an adaptation coefficient. The adjustment constitutes an estimate of the gradient of the mean squared error of the output (when compared to some desired output) with respect to the compensator coefficients. With knowledge of the gradient, the coefficients are then adjusted in a direction of the negative gradient, which is a direction toward the point of minimum mean squared error.
A further known technique for improving compensation actions is termed "back-propagation through time" and involves calculating the effective error associated with each control sample generated by the compensator during the closed loop system's response to some disturbance. Since each compensator command signal affects not only the next position error signal but also all future position error signals (to some degree), back-propagation through time attempts to determine the overall error attributable to each compensator command signal. This "effective error" is then used in the LMS algorithm to update the weights.
Back propagation through time has been mainly applied in the field of neural networks which include nonlinear functional blocks for achieving non linear transfer functions or decision circuits that could not be accomplished linearly. The back propagation procedure essentially takes an average of the compensator's contribution to present and later errors for each command signal, and uses this average to adjust the compensator in a direction that reduces the average error.
The determination of back propagation correction values is accomplished in the prior art by analyzing a closed loop system as a feed forward system. This is done by first generating a digital filter model of the plant and then applying an analytical technique known as `unfolding in time` to represent the feedback system as strictly a feedforward system for a finite number of samples. The plant and compensator elements are copied multiple times in cascade. Each plant and each compensator in the cascade sums the delayed and weighted signals from present and past inputs and outputs. Instead of taking these inputs and outputs from certain sample times, they are shown as being taken from certain stages in the cascade.
The inputs and outputs of the plant and compensator at any stage in the cascade are equivalent to the inputs and outputs at a corresponding time step during the response of the system. For example, the feedback of the position error signal from the output of the plant to the input of the compensator is no longer shown as a feedback of the system output to its input. It is shown instead as the feeding forward of the output of stage k to the input of stage k+1, where k represents the time index and the cascade index equivalently.
With the system unwrapped in time, as described above, the system can be analyzed as a completely feedforward system. As such, a generalized form of the LMS algorithm, known in the Neural Network literature as back propagation of errors or simply `back propagation`, can be applied to determine the contribution of each plant and compensator in the cascade to the overall error. This effective error is then used in the LMS algorithm to adjust the compensator at each stage in the cascade. Since, in reality, each compensator in the cascade is just a representation of the single compensator in the original closed loop system as it was unrolled in time, the compensator adjustment made at each stage in the cascade must be averaged into one final adjustment that is made on the real compensator. This calculation is normally done offline and completely within the confines of the computer or microprocessor which is controlling the system.
Back propagation through time is discussed in "Back propagation through time: What it is and how to do it", Paul J. Werbos, Proceedings of the IEEE, Vol. 78, No. 10, October 1990.
The use of a feed-forward network to derive back propagation values is both time consuming and employs substantial processing assets to achieve an effective network construct. It is also dependent on the accuracy of plant model (since the method requires a model of the plant through which to calculate the back propagation values).
Accordingly, it is an object of this invention to provide an improved control circuit for a disk drive transducer head actuator.
It is a further object of the invention to provide an improved control circuit for a disk drive transducer head actuator which employs the actuator itself instead of relying on a model of the actuator.
It is another object of this invention to provide an improved compensator for a disk drive transducer actuator, which compensator employs back propagation error correction without requiring the use of a back propagation network.
It is yet another object of this invention to provide an improved compensator for a disk drive transducer head actuator wherein weighted back propagation values are employed to enable the achievement of increased accuracy operations of the actuator mechanism.